Cross Validation For Selecting The Penalty Factor In Least Squares Model Averaging

In recent years,model averaging has attracted a lot of attention in the field of statistics and economics due to its good prediction effect.In the research on the theoretical properties of model averaging,people generally pay attention to the asymptotic optimization of selection weight.The asymptotic properties of the least squares model averaging are usually studied in two different cases:(1)all candidate models are under fitted;(2)the candidate model includes the true model.Existing studies have shown that the penalty factor ?n in the weight selection criteria plays a key role in the results.Simply speaking,in case 1,?n=2 is usually preferred,while in case 2,?n=2 will not be like ?n=log(n),which is asymptotically optimal,and ?n=log(n)is usually preferred when the sample size is large enough.Because the real situation is always unknown,it is difficult to choose the appropriate penalty factor in practice,however,there is little rigorous research on this problem in the existing literature.To solve this problem,this paper mainly studies the penalty factor selection method based on cross validation.Firstly,we discuss the conventional cross validation based method for selecting the penalty factor log(n)and 2.However,through the analysis of its asymptotic properties,we find that this method has some problems in theory.Then,we propose a new improved cross validation method for model averaging,and prove that the improved method has adaptive asymptotic optimality.In other words,the optimal weight obtained by the cross validation method has asymptotic optimality in both case 1 and case 2.Then,we further propose and discuss two other new cross validation methods.Finally,a large number of simulation experiments and case analysis are done,and the experimental results verify the effectiveness of the three improved methods.In addition,we also discuss the advantages and disadvantages of the three methods through the experimental results.